Question: $h(x) = -x^{3}-2x^{2}+x-4$ $g(x) = -7x^{2}-h(x)$ $ h(g(5)) = {?} $
Solution: First, let's solve for the value of the inner function, $g(5)$ . Then we'll know what to plug into the outer function. $g(5) = -7(5^{2})-h(5)$ To solve for the value of $g$ , we need to solve for the value of $h(5)$ $h(5) = -5^{3}-2(5^{2})+5-4$ $h(5) = -174$ That means $g(5) = -7(5^{2})-(-174)$ $g(5) = -1$ Now we know that $g(5) = -1$ . Let's solve for $h(g(5))$ , which is $h(-1)$ $h(-1) = -(-1)^{3}-2(-1)^{2}-1-4$ $h(-1) = -6$